1. Field of the Invention
This invention relates to an interference fringe analyzing method and an apparatus for the same for use in a holographic interferometer system which makes use of computer generated holograms, the method and the apparatus being capable of correcting any deviation of a wave surface due to an error in the disposition of an object to be examined or the disposition of a computer generated hologram.
2. Description of the Prior Art
A type of holographic interferometer has been known, which is based on a method of measuring the shape of a surface of an aspherical optical element, which makes uses of, as reference hologram, a so-called "computer generated hologram" made by electron beam writing or the like by calculating a hologram pattern by an electronic computer from an optical set value of a reference aspherical surface; makes light having a wave surface reflected at or transmitted through an aspherical optical element to be examined and diffracted by the reference hologram interfere with reference light; and accurately measures, from the amount and shape of interference fringes thereof, a manufacturing error of the aspherical optical element.
As a method of adjusting the dispositions of the object to be examined and the reference hologram in the holographic interferometer, two methods have been known: one in which both the object and the reference hologram are moved while interference fringes are being observed; and one such as that disclosed in the thesis "Testing aspheric surfaces with computer-generated holograms: analysis of adjustment and shape errors" by B. Dorband et al (Applied Optics, Vol. 24, No. 16 p.p.2604 to 2611) in which fluctuations of the object wave due to inclinations of the reference plane of the holographic interferometer relative to the x- and y- axes, inclinations of the object relative to the X- and Y- axes, an eccentricity or decenter of the object in the X-Y plane, and an eccentricity of the reference hologram in the x-y plane are preliminarily simulated by ray tracing; the difference between a coefficient of the Zernike polynomial in this simulation and a coefficient of the Zernike polynomial at the time when the object and the reference hologram are disposed in the normal positions is obtained; this difference is subtracted as differentiation of the object wave from an observed wave surface.
In the former type of method, namely, a method in which the object and the reference hologram are adjusted while interference fringes are being observed, an interference pattern resulting from an error in the disposition of the object also changes depending upon five components i.e. the eccentricity error of the object in the X-Y plane, the inclination of the object relative to X- and Y- axes, and the defocusing. Therefore, the disposition adjustment in accordance with this method requires a great deal of experience and skill. To effect the adjustment, it is necessary to move the object in a trial-and-error manner, resulting in a prolonged measurement time.
The latter type of method, namely, the method by Dorband et al necessitates a preliminary step of performing ray tracing with respect to eight variables and therefore requires a very large amount of calculation and a very long calculation time for this step. In addition, in this method, the differential coefficient of each of the inclinations of the reference plane and the object, the eccentricity of the object and the eccentricity of the reference hologram has a small degree of independency. For this reason, there is an increased possibility of errors in the calculations of the components if the calculations are performed by the method of least squares. Moreover, it is not possible to perform the calculations for the simulation unless all of the optical dimensions of the ideal shape of the object and the interferometer are given.